Part A: To compare the slopes of the two functions, we need to determine the slope of each function. The slope of a linear function can be found using the formula:
slope = (change in y) / (change in x)
For the function f(x), we can determine the slope by selecting any two points from the table and calculating the change in y divided by the change in x. Let's choose the points (-1, -5) and (1, 3):
slope of f(x) = (change in y)/(change in x) = (3 - (-5)) / (1 - (-1)) = 8 / 2 = 4
So, the slope of f(x) is 4.
For the function g(x), we can determine the slope by looking at the equation g(x) = 2x - 7. The coefficient of x in the equation represents the slope. Therefore, the slope of g(x) is 2.
Comparing the two slopes, we see that the slope of f(x) is 4, while the slope of g(x) is 2. Therefore, the slope of f(x) is greater than the slope of g(x).
Part B: To determine which function has a greater y-intercept, we need to compare the y-intercepts of the two functions. The y-intercept is the value of y when x = 0.
For f(x), we can see from the table that when x = 0, f(x) = -1. So, the y-intercept of f(x) is -1.
For g(x), we can refer to the equation g(x) = 2x - 7. When x = 0:
g(x) = 2(0) - 7 = -7
So, the y-intercept of g(x) is -7.
Comparing the y-intercepts, we see that the y-intercept of f(x) is -1, while the y-intercept of g(x) is -7. Therefore, g(x) has a greater y-intercept than f(x).